' t0 
the 
he 
as 
ly 
  
«rí(x, t)r (x', t'Jo z «r(x, tr^ (x', t!J5»s(x = x") (11) 
where the brackets denote ensemble averaging, the expected value of the 
image intensity is given by 
| [ie x)i (x", x)» dx' dx" 
fr w) dx! (12) 
fp(x!, 0) = <|r(x, 4)|^ (13) 
Il 
«I(x)» 
Il 
where 
is the Doppler spectrum of the surface reflectivity. 
The simulation procedure suggested by this model is therefore to com- 
pute the Doppler spectrum of the surface reflectivity at each grid cell in 
the scene, and then to map the radar cross section onto the image using 
the Doppler spectrum to control the mapping, as illustrated in Figure 1. 
The Doppler spectrum is approximated by a Gaussian-like function with a 
center location eg and a width Aw. The total area under the spectrum is 
equal to the radar cross section og(x'). 
Scene SAR Image 
Range 
  
Azimuth 
Figure 1. Illustration of SAR Mapping Function, Including Azimuthal 
Shifting and Smearing Effects 
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